A copy editor or line editor focuses on improving sentences and grammar, as well as suggesting other ways of rephrasing ideas, and providing comment on anything else they pick up. Non-fiction books often use multiple styles, for example, chapter headings, sub-headings, action points, bullet points, call-outs and examples, so these will be examined at this phase.
Stephen, you’re right, and I think much of the confusion about editing and its pricing stems from the fact that editors offer a range of services (in addition to a range of experience). It might be best to view editing on a spectrum from broad (developmental) to detailed (copyediting and proofreading). And it’s always best to have as clear an idea as you can about the kind of editing you believe you need.
As one person who “woke up and decided since I’m published and an English major, I should be an editor,” I can see your point of being only one type of editor. I’m not a good copyeditor at all and don’t offer my services for that situation. It’s funny that you would say a traditionally published type editor would be better than the independently published editor. I found this to be totally untrue since I have worked with both. My traditional editors from St. Martins Press and Bantam books working a total of 35 years in the industry, was the worst editor of all. My independently published editor/book coach, is the most knowledgeable. So there is a bit of a disparage. It’s not an absolute science, editing.
Regarding your last question, I know of no editor who gives a money-back guarantee for occasional errors that happen to slip through or for a different opinion by a later editor. I’m afraid such things are just the nature of the publishing beast. But by having a shorter portion edited first, you will get a decent feel for whether someone is the right editor for you, and will be able to be confident in his or her work on your entire book.